The ode23 function is adapted from Chapter 7 of the book Numerical Computing with Matlab by Cleve Moler. The original source is at: http://www.mathworks.in/moler/ncm/ode23tx.m
The code carries the following notice:
Copyright 2012 Cleve Moler and The MathWorks, Inc.
The ode45 function is adapted from this implementation for Octave, and is available under the GPL.
http://users.powernet.co.uk/kienzle/octave/matcompat/scripts/ode_v1.11/ode45.m
The code carries the following notice:
Copyright (C) 2001, 2000 Marc Compere This file is intended for use with Octave. ode45.m is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2, or (at your option) any later version.
ode45.m is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details at www.gnu.org/copyleft/gpl.html.
These are implemented by Patrick O'Leary, and available under the MIT License.